# Help with Boolean algebra

Discussion in 'Homework Help' started by bigga, Aug 27, 2006.

1. ### bigga Thread Starter New Member

Aug 27, 2006
1
0
Prove i. AD + BD + BC + ABD = BC + D
ii. (x'y' + z)' + z + xy + wz = x + y + z

I'm new to Boolean algebra and I've tried all the rules for Boolean algebra without success. Help anyone?

2. ### Papabravo Expert

Feb 24, 2006
10,340
1,850
Consider the following identities:
Code ( (Unknown Language)):
1.
2. A' = A'B + A'B'   and
3. B  = BA' + BA
4.
5. Now
6. A'D + BD + B'C + AB'D  =
7. (A' + B + AB')D + B'C   =
8. (A'B + A'B' + A'B + AB + AB')D + B'C =
9. (1)D + B'C
10.
Show us what you got for the other one - eh?
I shouldn't have to do all the heavy lifting.

3. ### shivani New Member

Mar 31, 2010
2
0
a'd + bd + b'c + ab'd
= a'd + d(b+ab') + b'c
= a'd + d(a + b) + b'c
= a'd + ad + db + b'c
= d(a' + a) + db + b'c
= d + db + b'c
= d(1 + b) + b'c
= d + b'c

4. ### mps New Member

Feb 4, 2010
8
0
The 1st question is solved by 2 gentlemen
Now the 2nd question is wrong as the lhs is 1
the actual question must be

(x'y' + z')' + z + xy + wz = x + y + z